Experiments on the solution of the helmholtz equation using the finite element method and a variational approach in the case of domains of complicated boundary shape

Domains of ‘exotic’ boundary shape are of interest in several technological applications—acoustic and electromagnetic waveguides, solid propellant rocket cross-sections, printed circuit boards, etc.The present paper describes some experiments performed to determine the eigenvalues of a vibrating, ideal membrane.It is shown that the finite element method yields results which are in very good agreement with values determined by means of an analytical approach in the case of a membrane of a cardioidal shape.